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Emergent Quantum Euler Equation and Bose–Einstein Condensates

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Abstract

In this paper, proceeding from the recently developed way of deriving the quantum-mechanical equations from the classical ones, the complete system of hydrodynamical equations, including the quantum Euler equation, is derived for a perfect fluid and an imperfect fluid with pairwise interaction between the particles. For the Bose–Einstein condensate of the latter one the Bogolyubov spectrum of elementary excitations is easily reproduced in the acoustic approximation.

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Notes

  1. The more general case of charged particles in the present external electromagnetic field is a subject of our forthcoming paper.

  2. It should be noted, that there is no need to take into account the distribution of velocities, as distinct from the chapter 3.6 in [1].

  3. Development of this method for the modified Liouville equation in the de Broglie–Bohm theory is also a subject of our forthcoming paper.

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Acknowledgments

M. V. Eingorn wants to thank Prof. V. L. Kulinskii for very useful discussions. V. D. Rusov is sincerely grateful to participants of the seminar of the Akhiezer Institute for Theoretical Physics (KITP, Kharkov, Ukraine) for the benevolent atmosphere during the discussion and the fruitful comments. The work of M. V. Eingorn was supported in part by NSF CREST award HRD-0833184 and NASA Grant NNX09AV07A.

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Authors and Affiliations

  1. Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Shevchenko av. 1, Odessa , 65044, Ukraine

    Maxim V. Eingorn & Vitaliy D. Rusov

  2. Astronomical Observatory, Odessa National University, Dvoryanskaya st. 2, Odessa , 65082, Ukraine

    Maxim V. Eingorn

  3. Physics Department, North Carolina Central University, Fayetteville st. 1801, Durham, NC , 27707, USA

    Maxim V. Eingorn

Authors
  1. Maxim V. Eingorn
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  2. Vitaliy D. Rusov
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Correspondence to Maxim V. Eingorn.

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Eingorn, M.V., Rusov, V.D. Emergent Quantum Euler Equation and Bose–Einstein Condensates. Found Phys 44, 183–191 (2014). https://doi.org/10.1007/s10701-014-9782-4

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  • DOI: https://doi.org/10.1007/s10701-014-9782-4

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